Investments: the relationship between losses and amortization times

When investing in financial markets, the chances that the investment may lose value over a period of time are often underestimated and that it may take time to recoup momentary losses.

The deeper the loss, the more disproportionate energy to recover from the loss.

If I invest 100 euros and lose 10%, I find myself with 90 euros (if I keep the investment or liquidate it), so to return to 100 what return do I have to make?

I have to do eleven percent, because with a base of 90 euros, if I do 10% I find myself at 99.

This effect is amplified if I lose 20%, to return from 80 euros to 100 euros, I will have to do 25%.

Therefore, the losses are not exactly symmetrical to the gains that must be made to recover them.

If I find myself losing 50% of my investment, to return to 100 from 50, I have to double down, so it must be intuitive to the reader that the more the loss is amplified, the more energy to recover is high.

Figure 1: Relationship between loss and recovery

Of course, it is not uncommon for stock exchanges to lose more than 20%, but when it happens it is always advisable to ask questions, because if you simply go to 30%, the necessary recovery will almost double, if it arrives. 40% of the triple loss, and if it reached -50%, the gain needed to return to parity becomes four times greater than -20%.

But in addition to the loss and gain needed to recover it, it is also essential to take into account the time required to recover it.

In order to have an estimate of the time needed to recover the losses and especially to check if there is a relationship between the loss suffered and the time to recover it, I decided to analyze the MSCI world from 1970 to the present to analyze it. the behaviour. in periods of period loss (or as the Anglo-Saxons call it, from Drawdown).

Some mandatory methodological notes:

a) the index considered is MSCI World, which represents a better diversification of equity markets than the only S & P500, although the latter still represents the majority;

b) The reference currency used is the dollar because the euro did not exist in 1970;

c) the frequency of analysis is daily;

d) period from 31/12/1969 to 16/06/2022, the day of the analysis.

First curiosity, of 19170 days, there were 266 unique periods of loss of more than two days, of which 3 exceed 2300 days and only 4 periods of more than 1000 days.

No alternate text was provided for this image

Figure 2: Graph of losses and recoveries (ulcer index)

The “period of apnea” can be measured by the Ulcer Index, or the ulcer index that was invented by Peter Martin in 1984; this indicator actually calculates the area in Figure 2, that is, all loss periods between a previous and next maximum.

The chart eliminates yields that create a new maximum growth, leaving only the negatives and those needed to return to the previous maximum value.

The ulcer index actually calculates the area underlying these two values, and obviously the higher the value, the worse the time series.

The Ulcer Index is useful and an alternative to the volatility indicator, but it does not provide information on the relationship between loss and recovery time.

So I plotted each loss, in percentage terms, on the Y axis and the days of free diving on the X axis on a Cartesian graph.

No alternate text was provided for this image

Figure 3: Relationship between MSCI World loss and recovery time

As you can see, there is a relationship between the loss of the index and the period of apnea from a minimum before the next.

Obviously, a greater loss corresponds to a greater number of days of apnea, which for clarity consists of a period in which the index loses value and reaches a minimum and a period in which the index grows again. up to the new maximum.

These days the MSCI World index has lost more than 20%, a threshold that many consider as the limit beyond which to enter a market called “bearish”.

So, I have listed in a table the 15 times that the MSCI World Index expressed in dollars has lost more than 10% to try to understand these dynamics in the most pronounced cases of loss and also try to imagine what lies ahead. .

No alternate text was provided for this image

Figure 4: Table of periods with a loss of more than 10%

Also analyzing the days needed to reach the minimum value, and then start again towards new highs, is useful to understand the typical rate of decline of the stock market.

No alternate text was provided for this image

Figure 5: Relationship between the maximum period loss and the days required to reach it

The blue dot indicates the moment today, with the MSCI world losing 22% in 164 days, all in all the rate of fall of the market is in line with the previous ones, so it is unlikely that an increase is expected to V over the next few months, as it occurred in 2020 as a result of the spread of VOCID, a period in which the decline was very rapid and the rise to new highs was also very rapid.

But it is very interesting to understand what awaits us in the coming months is to analyze the periods that were necessary to recover the previous losses.

Obviously, as seen before, a loss of 50% corresponds to a return needed to recover the loss of 100%, so the following graph shows the returns that have actually been made and how many days it took to achieve -the, in the different markets. phases ..

No alternate text was provided for this image

Figure 6: Relationship between the performance to be recovered and the time required

This chart shows that there is a clear relationship in the stock market between the loss suffered and the time required to recover it.

To give an example, with + 30% needed today to recover -22%, assuming that we have bottomed out and from there the markets start again (attention that is a hypothesis, the writer does not think at all that the market has bottomed out) it is reasonable to expect a recovery time of 466 days, following the formula derived from the regression line described in Figure 6:

No alternate text was provided for this image

Where G are the expected days to recover the loss

EP is the percentage of loss suffered

From this logic it follows that we cannot know whether the accumulated loss so far corresponds to the minimum of the period, but for each minimum that derives from it we can estimate the expected time to recover it.

Consequently it follows that the worse the loss, the longer I will have to wait to recover it as can be seen in the chart below.

No alternate text was provided for this image

Figure 7: Relationship between loss and estimated time to recovery

Some considerations:

a) The analysis presented here represents an estimate based on historical data, there is no guarantee that the market will recover within or around the estimated values;

b) There is no hypothesis that can establish that the current loss should be considered a minimum period, in fact, everything suggests that the loss will be deeper than the current one;

c) Failure to sell does not mean that the loss is not real; the loss is such even if the underlying asset is not sold, it is simply not realized, but in any case it is real and the market will have to make the recovery corresponding to Figure 1 to recover the initial value;

But above all, it is not entirely true that it should not be sold in phases of market decline; it is necessary to assess whether it is advisable to stop losses to prevent them from getting worse, wait for a time when it is clearer that the market is recovering and reinvest at that time: the time to win the market will always offer, but when the losses are too deep , you have to spend time and money just to get them back, instead of making money.

Going back to the initial example, if I have lost 20% and it is the minimum period, I will have to wait an average of 388 days to recover the loss, if the minimum is at 30% loss, I will have to wait about 668 days. days to recover, if the loss is 40% the estimated waiting time will be about 1041 days, while if the loss becomes 50% the estimated recovery time will increase to 1555 days.

Therefore, in a situation of uncertainty such as the current one, the risk of exacerbating the loss still runs the risk of prolonging the recovery time, as well as the ulcer that results from the increase. of the loss, so it may be taken into account to alleviate the investment while waiting for the market to make its minimum and then return, although a little later, it could be a solution to consider; at least this action leads to a certain result, the reduction of risk at a time when it is especially high.

I hope this work allows you to think analytically without getting caught up in emotions.

Edited by Daniel Bernardimanaging director of Partners DIAMAN

Leave a Comment